PiecewiseChebyshev
class PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')
Bases: qiskit.circuit.library.blueprintcircuit.BlueprintCircuit
Piecewise Chebyshev approximation to an input function.
For a given function and degree , this class implements a piecewise polynomial Chebyshev approximation on qubits to on the given intervals. All the polynomials in the approximation are of degree .
The values of the parameters are calculated according to [1] and see [2] for a more detailed explanation of the circuit construction and how it acts on the qubits.
Examples
import numpy as np
from qiskit import QuantumCircuit
from qiskit.circuit.library.arithmetic.piecewise_chebyshev import PiecewiseChebyshev
f_x, degree, breakpoints, num_state_qubits = lambda x: np.arcsin(1 / x), 2, [2, 4], 2
pw_approximation = PiecewiseChebyshev(f_x, degree, breakpoints, num_state_qubits)
pw_approximation._build()
qc = QuantumCircuit(pw_approximation.num_qubits)
qc.h(list(range(num_state_qubits)))
qc.append(pw_approximation.to_instruction(), qc.qubits)
qc.draw(output='mpl')
References
[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).
Optimizing Quantum Circuits for Arithmetic. arXiv:1805.12445
[2]: Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022).
Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation. ACM Transactions on Quantum Computing 3, 1, Article 2
Parameters
- f_x (
Union[float,Callable[[int],float]]) – the function to be approximated. Constant functions should be specified as f_x = constant. - degree (
Optional[int]) – the degree of the polynomials. Defaults to1. - breakpoints (
Optional[List[int]]) – the breakpoints to define the piecewise-linear function. Defaults to the full interval. - num_state_qubits (
Optional[int]) – number of qubits representing the state. - name (
str) – The name of the circuit object.
Attributes
ancillas
Returns a list of ancilla bits in the order that the registers were added.
Return type
List[AncillaQubit]
breakpoints
The breakpoints for the piecewise approximation.
Return type
List[int]
Returns
The breakpoints for the piecewise approximation.
calibrations
Return calibration dictionary.
The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}
Return type
dict
clbits
data
degree
The degree of the polynomials.
Return type
int
Returns
The degree of the polynomials.
extension_lib
Default value: 'include "qelib1.inc";'
f_x
The function to be approximated.
Return type
Union[float, Callable[[int], float]]
Returns
The function to be approximated.
global_phase
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 2502
metadata
The user provided metadata associated with the circuit
The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.
Return type
dict
num_ancillas
Return the number of ancilla qubits.
Return type
int
num_clbits
Return number of classical bits.
Return type
int
num_parameters
Return type
int
num_qubits
Return number of qubits.
Return type
int
num_state_qubits
The number of state qubits representing the state .
Return type
int
Returns
The number of state qubits.
op_start_times
Return a list of operation start times.
This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.
Return type
List[int]
Returns
List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.
Raises
AttributeError – When circuit is not scheduled.
parameters
Return type
ParameterView
polynomials
The polynomials for the piecewise approximation.
Return type
List[List[float]]
Returns
The polynomials for the piecewise approximation.
Raises
TypeError – If the input function is not in the correct format.
prefix
Default value: 'circuit'
qregs
A list of the quantum registers associated with the circuit.